Genre: ken (拳)

David Waterhouse in his scholarly catalogue of the Harunobu prints in the Museum of Fine Arts in Boston gives the most detailed and informative description of the game of ken we have found anywhere. It appears on pages 163-164 if volume 1, the text. Much of this is as follows:

"There are at least twenty varieties of ken, a type of parlour game which is found in many other countries, but which, as Thomas Crump remarks, "is still entrenched in Japanese culture in a way unparalleled elsewhere"... Under various names, ken (literally 'fist') is known to have been played in China during the Hàn and Táng times; it is supposed to go back to the Zhōu period; and it may have originated in China. The earliest Japanese forms of the game, known generically as mushi-ken, 'ken of small animals'), [sic] are attributed to the Nara and Heian periods...; there is iconographic evidence for it from the early 14th century (from Ishiyamadera engi emaki); and under Chinese influence it started to become immensely popular in urban circles in the middle of the eighteenth century. In the West, it seems to be best known as "Scissors - Paper - Stone".

In the terminology of game theory, most of the Japanese games are zero-sum two-person games with mixed strategies; and in kitsune-ken or in jan-ken (the most popular at the present day)... In plain language, Scissors cuts Paper, Paper covers Stone, but Stone grinds Scissors; or, in kitsune-ken, Headman beats Gun, Gun beats Fox, but Fox beats Headman. Using the fingers of one hand (in jan-ken), or both hands (in kitsune-ken), the players mime gestures to indicate their moves, matching them with calls. Unless both make the same move, the winner is the one who plays the higher number, positive or negative.

In technical terms, this game lacks a saddle point; so that over a series of games the best strategy for both players is to use an equal mixture of all three moves. (For an explanation of the mathematics underlying this game, whose simplicity made it one of the first to be analysed by game theorists, see Von Neumann & Morgenstern 1953... [et al.] For an explanation of the hand-gestures in each game, and its matching calls (yobigoe), see Morisue & Hinoshi 1957, p. 211.)
[This last paragraph is followed by a chart, Table 1 - omitted here.]
The above are examples of what Japanese writers call misukumi-ken (or sansukumi-ken), 'three-clench ken; or... 'ken of the three who are afraid of one another'. Since they are logically simple, it is natural to assume that they represent the oldest forms of the game. However, another group of ken games, known in Japanese as kazu-kenhon-ken, is said to have been introduced to Japan by Chinese visitors to Nagasaki, presumably in the early eighteenth century... and another name for it was Nagasaki-ken. The game quickly spread to Edo; and, according to Kiyū shōran, "in the Yoshiwara and other places, during the Kyōhō period (1716-36)), something called ken sumō (ken wrestling') was popular, and the courtesan Tamigiku was expert at this"... Tamagiku, who belonged to the Manjiya, is referred to elsewhere for her prowess in these competitions; and ken sumō is mentioned in a sharebon of 1770, Tatsumi no sono... in which a visitor to Fukugawa plays against one of the girls, using special calls appropriate to hon-ken. A text-book of 1830, Ken hitori keiko, illustrated by Kitagawa Toyoharu, explains in detail how to play the game.

In hon-ken, if one points the thumb alone, it counts for 'one' (ikkō); opening the thumb and forefinger together counts 'two' (ryan); pointing the other three fingers together counts 'three' (san); opening four fingers together, but keeping the thumb curled up, counts 'four' (sū); opening all five digits together counts 'five' (go); and closing the fist completely counts 'six' (mui). In addition to this, calls for higher numbers are used: 'seven' (chie); 'eight' (pama); 'nine' (kwai); 'ten' (tōrai; and, in the original game but already obsolete by 1830, 'zero' (mu). The calls are all in Tō-on pronunciation, and Ken hitori keiko gives several alternative calls for each number. Ōta Nanpo, in Hannichi kanwa, illustrates gestures and calls from a manual published in 1746... and together with his friends he even devised a kind of kazu-ken, which he describes in Shichi-ken zushiki (1779)...

The two players are known as kō and otsu. Each makes a gesture with his right hand, and a call which is his guess at the sum of his move and his opponent's. If both guess right, or if neither does, the result is inconclusive; otherwise, one player wins the round, and keeps his score (kazutori) on the fingers of his left hand. Ten rounds constitute a game. It will be seen that the principles of this game are quite different from that of the previous types, in that there is not circular relationship among the different moves; also that the number of moves open to each player, combining gesture and call, is much greater. In fact, a pay-off matrix for hon-ken would require 14,641 [variations], and the strategies would be correspondingly harder to calculate."